Find an AM radio and tune it to an area of the dial where you hear static.

Now hold the battery near the antenna and quickly tap the two terminals of the battery with the coin (so that you connect them together for an instant).

You will hear a crackle in the radio that is caused by the connection and disconnection of the coin.

Your battery/coin combination is a radio transmitter! It's not transmitting anything useful (just static), and it will not transmit very far (just a few inches, because it's not optimized for distance). But if you use the static to tap out Morse code, you can actually communicate over several inches with this crude device!